Degree-Constrained -Minimum Spanning Tree Problem

Table 3

Numerical results obtained with and for random graphs using and .

#													Gaps
			Opt		Time	LP	Time	Opt		Time	LP	Time	%	%
1	50	10	46.86	42	2.29	43.38	0.23	46.86	340	1.25	43.38	0.20	7.43	7.43
2		20	113.97	2161	16.65	109.46	0.25	113.97	999	11.42	109.46	0.27	3.96	3.96
3		30	204.35	116	1.67	197.61	0.19	204.35	2024	14.65	197.61	0.19	3.30	3.30
4		50	459.09	123	1.00	444.77	0.25	459.09	629	3.87	447.87	0.20	3.12	2.44
5	100	25	115.44	358	46.71	114.54	0.53	115.44	97	54.60	114.54	0.70	0.78	0.78
6		50	263.95	1243	73.63	261.02	0.51	263.95	668	77.50	261.02	0.75	1.11	1.11
7		75	454.44	459	143.16	449.51	0.55	454.44	525	111.53	449.51	0.67	1.08	1.08
8		100	749.75	24	22.56	728.70	2.29	749.75	0	40.36	734.84	0.59	2.81	1.99
9	200	50	162.55	479	3995.62	160.36	2.21	162.55	920	2835.21	160.36	3.29	1.35	1.35
10		100	378.43	479	2671.16	373.28	3.81	—	—	7200	373.28	3.68	1.36	—
11		150	652.86	479	2097.25	642.84	4.71	652.86	465	1663.29	642.84	3.49	1.53	1.53
12		200	1049.25	607	505.27	1030.04	30.11	1049.25	502	1490.46	1034.23	3.21	1.83	1.43
1	50	10	52.22	5	1.01	46.42	0.25	52.22	190	1.73	46.30	0.20	11.12	11.34
2		20	134.08	379	3.43	129.90	0.33	134.08	1515	21.95	129.71	0.20	3.12	3.26
3		30	240.30	235	7.35	239.32	0.28	240.30	736	19.08	239.32	0.20	0.41	0.41
4		50	564.37	488	20.20	557.48	0.28	564.37	1647	42.00	557.08	0.19	1.22	1.29
5	100	25	123.71	1067	248.12	121.55	1.50	123.71	1933	237.10	121.54	0.70	1.74	1.75
6		50	287.78	1676	632.83	285.35	2.84	287.78	857	356.21	285.31	0.81	0.84	0.86
7		75	529.56	0	8.88	529.31	3.23	529.56	1050	639.40	529.31	0.76	0.05	0.05
8		100	—	—	7200	914.60	4.13	—	—	7200	914.63	0.89	—	—
9	200	50	184.29	10	228.02	184.29	13.13	—	—	7200	184.29	3.81	0	—
10		100	—	—	7200	435.45	26.49	—	—	7200	435.45	6.61	—	—
11		150	—	—	7200	774.76	55.04	—	—	7200	774.76	6.62	—	—
12		200	1285.32	1045	1408.71	1284.58	94.68	—	—	7200	1284.58	4.15	0.06	—

—: no solution found.